Internal problem ID [5424]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 18. Linear equations with variable coefficients (Equations of second order).
Supplemetary problems. Page 120
Problem number: 33.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x y^{\prime \prime }-3 y^{\prime }+\frac {3 y}{x}=x +2} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(x*diff(y(x),x$2)-3*diff(y(x),x)+3*y(x)/x=x+2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-2 x -2 \ln \left (x \right )+c_{1} x^{2}+2 c_{2} \right ) x}{2} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 30
DSolve[x*y''[x]-3*y'[x]+3*y[x]/x==x+2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} x \left (2 c_2 x^2-2 x-2 \log (x)-1+2 c_1\right ) \]